pythonpython-2.7fractals

How to generate a fractal graph of a market in python

I wish to generate this in python:

http://classes.yale.edu/fractals/RandFrac/Market/TradingTime/Example1/Example1.html

but I'm incredibly stuck and new to this concept. Does anybody know of a library or gist for this?

enter image description here

Edit: From what I can understand is that you need to split the fractal in 2 every time. So you have to calculate the y-axis point from the line between the two middle points. Then the two sections need to be formed according to the fractal?

Solution

  • Not 100% sure what you are asking, but as I understood from your comments, you want to generate a realistically looking stock market curve using the recursion described in the link.

    As far as I understood the description in the linked page and some of the parent pages, it works like this:

    1. You are given a start and an end point and a number of turning points in the form (t1, v1), (t2, v2), etc., for example start=(0,0), end=(1,1), turns = [(1/4, 1/2), (3/4, 1/4)], where ti and vi are fractions between 0 and 1.
    2. You determine the actual turning points scaled to that interval between start and end and calculate the differences between those points, i.e. how far to go from pi to reach pi+1.
    3. You shuffle those segments to introduce some randomness; when put together, they still cover exactly the same distance, i.e. they connect the original start and end point.
    4. Repeat by recursively calling the function for the different segments between the new points.

    Here's some Python code I just put together:

    from __future__ import division
from random import shuffle

def make_graph(depth, graph, start, end, turns):
    # add points to graph
    graph.add(start)
    graph.add(end)

    if depth > 0:   
        # unpack input values
        fromtime, fromvalue = start
        totime, tovalue = end

        # calcualte differences between points
        diffs = []
        last_time, last_val = fromtime, fromvalue
        for t, v in turns:
            new_time = fromtime + (totime - fromtime) * t
            new_val = fromvalue + (tovalue - fromvalue) * v
            diffs.append((new_time - last_time, new_val - last_val))
            last_time, last_val = new_time, new_val

        # add 'brownian motion' by reordering the segments
        shuffle(diffs)

        # calculate actual intermediate points and recurse
        last = start
        for segment in diffs:
            p = last[0] + segment[0], last[1] + segment[1]
            make_graph(depth - 1, graph, last, p, turns)
            last = p
        make_graph(depth - 1, graph, last, end, turns)

from matplotlib import pyplot
depth = 8
graph = set()
make_graph(depth, graph, (0, 0), (1, 1), [(1/9, 2/3), (5/9, 1/3)])
pyplot.plot(*zip(*sorted(graph)))
pyplot.show()

    And here some example output:

    enter image description here